All genuinely entangled stabilizer subspaces are multipartite fully nonlocal

Understanding which entangled states give rise to Bell nonlocality and thus are resourceful in the device-independent framework is a long-stanging unresolved problem. Here we establish the equivalence between genuine entanglement and genuine nonlocality for a broad class of multipartite (pure and mixed) states originating from the stabilizer formalism. In fact, we prove that any (mixed) stabilizer state defined on a genuinely entangled subspace is multipartite fully nonlocal meaning that it gives rise to correlations with no contribution from local hidden variable models of any type. Importantly, we also derive a lower bound on genuine nonlocality content of arbitrary multipartite states, opening the door to its experimental estimation.